Inferenza statistica per il modello CIR multifattoriale: un’ analisi del mercato delle Eurolire

Abstract

Cox, Ingersoll and Ross (1985) is one of the best known models of the term structure of interest rates. In this article I show how to exploit its exponential affine structure to restate the model in state space form, and how to estimate the parameters using the Kalman filter. The statistical properties of this approach are not known, since the model is not gaussian in the transition equation. However, it is known that in this framework the Kalman filter provides the best estimates of the state variables among those wich are linear functions of observations. For this reason it is reasonable to expect that the results be at least approximatively valid. This conjecture is confirmed by the result of a Monte Carlo experiment detailed in appendix. This approach has many advantages. First , it is possible to use the prices of a large number of financial assets, and at the same time to have parameters constant through time. Moreover, it is not necessary to assume that the state variables be observed: on the contrary , tha Kalman filter allows to extract from the observations (the spot rates) the in sample trajectory of the state variables , and to predict the future values. This article estimates the CIR model with 1 or 2 factors using weekly observations (ranging from 1986 to 1994) about 6 rates observed on the Eurolire market.